Don't use validation show if for this.
Just use:
<?php
if (isset($_POST)) {
?>
<table width="265" border="0" cellpadding="0" cellspacing="0">
<tr>
<td width="265" align="left" bgcolor="#FFFFCC" class="red">(Password successfully changed)</td>
</tr>
</table>
<?php
}
?>
Validation show if server behavior will never do anything when no validations fail at all. At that point validations are cleared and it is as if they never happened. The code above will work in that case instead.